Handbook on Import Risk Analysis for Animals and Animal Products

136 Pages·2012·1.51 MB·English

Handbook on
Import Risk Analysis
for Animals and Animal Products

Volume 2
1st Edition, 2004
Quantitative risk assessment

Published by
The World Organisation for Animal Health
(OIE)
All OIE (World organisation for animal health) publications are protected by
international copyright law. Extracts may be copied, reproduced, translated, adapted or
published in journals, documents, books, electronic media and any other medium
destined for the public, for information, educational or commercial purposes, provided
prior written permission has been granted by the OIE.
The designations and denominations employed and the presentation of the material in
this publication do not imply the expression of any opinion whatsoever on the part of the
OIE concerning the legal status of any country, territory, city or area or of its authorities,
or concerning the delimitation of its frontiers and boundaries.
The views expressed in signed articles are solely the responsibility of the authors. The
mention of specific companies or products of manufacturers, whether or not these have
been patented, does not imply that these have been endorsed or recommended by the
OIE in preference to others of a similar nature that are not mentioned.

© Copyright OIE
World organisation for animal health
12, rue de Prony, 75017 Paris, France
Tel.: [phone]
Fax: [phone]
http://www.oie.int
Volume I, First Edition (2004), ISBN : 92-9044-629-3
Second Edition (2010), ISBN:978-92-9044-807-5
Reprinted (2012):
Volume 2, First Edition (2004): ISBN 92-9044-626-9 (2004)
Reprinted (2010 & 2012): ISBN: 978-92-9044-626-2

Cover: © P. Blandín, OIE
Contents

Volume 2. Quantitative risk assessment
Authors
Acknowledgments

Chapter 1: An introduction to quantitative risk analysis ................................. 1
Introduction .............................................................................................................................. 1
Deterministic (point estimate) risk assessment ............................................................. 2
Probabilistic risk assessment (Monte Carlo simulation) ............................................. 5
Sampling values from a probability distribution ........................................................... 7
Differentiating variability and uncertainty ...................................................................... 7
Chapter 2: Probability and probability distributions ....................................... 11
Defining probability ............................................................................................................. 11
Classical probability............................................................................................................... 11
Empirical probability (relative frequency) ......................................................................... 11
Subjective probability ........................................................................................................... 11
The rules of Probability ....................................................................................................... 12
Independence ......................................................................................................................... 12
Conditional probability ......................................................................................................... 12
Mutually exclusive events ..................................................................................................... 13
Independent events that can occur simultaneously ......................................................... 13
Probability distributions ..................................................................................................... 14
Random variables .................................................................................................................. 14
Discrete distributions ............................................................................................................ 14
Continuous distributions ...................................................................................................... 15
Chapter 3: Theorems providing a basis for probabilistic risk
assessment ................................................................................................................................ 19
Binomial theorem ................................................................................................................. 19
Central limit theorem ........................................................................................................... 22
The normal distribution ....................................................................................................... 22
Defining the central limit theorem ..................................................................................... 25
Population mean (μ) and population standard deviation () are known ...................... 27
Population mean (μ) and population standard deviation () are not known ............... 28
Estimating the number of individuals (n) required to achieve a fixed total quantity .. 29
Bayes’ theorem ....................................................................................................................... 30
Chapter 4: Useful probability distributions ........................................................... 33
Distributions used to model a binomial process ......................................................... 33
Binomial distribution ............................................................................................................ 34
Beta distribution .................................................................................................................... 35
Negative binomial distribution ............................................................................................ 36
Distributions used to model a Poisson process ........................................................... 37
Poisson distribution .............................................................................................................. 38
Gamma distribution .............................................................................................................. 39
Handbook on Import Risk Analysis for Animals and Animal Products, Volume 2, 2004 I
Exponential distribution ...................................................................................................... 40
Estimating a lower bound for β, the mean interval between events,
when no events have been observed .................................................................................. 41
Estimating the probability of at least one event in an interval ....................................... 41
Cumulative distribution ........................................................................................................ 42
Discrete and discrete uniform distributions ...................................................................... 43
General distribution .............................................................................................................. 43
Histogram distribution ......................................................................................................... 43
Hypergeometric distribution ............................................................................................... 44
Lognormal distribution ........................................................................................................ 45
Normal distribution .............................................................................................................. 46
PERT (Beta PERT) distribution ......................................................................................... 47
Triangular distribution .......................................................................................................... 49
Uniform (rectangular) distribution ..................................................................................... 50
Chapter 5: Probability processes and calculations ............................................ 51
Expressing probability: the binomial versus the hypergeometric process .......... 51
Binomial probability calculations .................................................................................... 52
The probability of including at least one infected animal in a consignment ................ 53
Hypergeometric probability calculations ...................................................................... 59
Chapter 6: Determining a distribution to represent a variable .................. 65
Sources of information ......................................................................................................... 65
Determining a distribution where there are abundant representative data ......... 65
Parametric techniques ........................................................................................................... 66
Non-parametric techniques ................................................................................................. 67
Determining a distribution where there are few representative data ..................... 67
Classical statistics ................................................................................................................... 68
Bootstrap simulation ............................................................................................................. 70
Using expert opinion to determine a distribution where data are non-existent,
scarce or not representative ................................................................................................ 73
Bias .......................................................................................................................................... 74
Expert disagreement ............................................................................................................. 74
Eliciting expert opinion ........................................................................................................ 74
Choosing an appropriate distribution to model expert opinion .................................... 76
Determining a distribution by combining empirical data and expert opinion ... 76
Bayesian inference ................................................................................................................. 76
Prior distributions ................................................................................................................. 78
Likelihood functions ............................................................................................................. 80
Posterior distributions .......................................................................................................... 80
An example of a Bayesian inference calculation: Developing a distribution for an
uncertain parameter p, the prevalence of infection in a chicken flock .......................... 81
An example of a Bayesian inference simulation ............................................................... 84
Chapter 7: An introduction to second order modelling.................................. 87
Separating variability and uncertainty ........................................................................... 87
Can a second order model be justified? ............................................................................. 88
Calculating variability, simulating uncertainty ................................................................... 89
Simulating both variability and uncertainty ....................................................................... 92
II Handbook on Import Risk Analysis for Animals and Animal Products, Volume 2, 2004
Chapter 8: Guidelines for developing a quantitative risk assessment
model ............................................................................................................................................ 93
Determining the scope of the risk analysis ........................................................................ 93
The population(s) of interest ............................................................................................... 94
Depicting the model graphically ......................................................................................... 94
Simplicity ................................................................................................................................ 99
Accounting for independence between units .................................................................... 99
Independence and dependence or correlation between variables ............................... 100
Data and information ........................................................................................................ 101
Modelling a variable ........................................................................................................... 101
Separating uncertainty and variability .............................................................................. 101
Ensuring a model generates plausible scenarios ............................................................ 102
Verifying calculations ......................................................................................................... 102
Sensitivity analysis .............................................................................................................. 102
Presenting the results ......................................................................................................... 103
Peer review .......................................................................................................................... 104
Appendices ............................................................................................................................ 105
Appendix 1: Table of exact binomial confidence limits ....................................... 105
Appendix 2: How to calculate exact binomial confidence limits ...................... 120
Appendix 3: Calculating binomial confidence limits not contained
in Appendix 1 ............................................................................................ 121
Bibliography ......................................................................................................................... 123
Index.......................................................................................................................................... 125
_____________
Handbook on Import Risk Analysis for Animals and Animal Products, Volume 2, 2004 III
Author
Noel Murray
Ministry of Agriculture and Forestry
New Zealand
Editorial assistance
Stuart C. MacDiarmid
Ministry of Agriculture and Forestry
New Zealand
Marion Wooldridge
Veterinary Laboratories Agency (Weybridge)
United Kingdom
Bruce Gummow
Faculty of Veterinary Science
University of Pretoria
South Africa
Randall S. Morley
Canadian Food Inspection Agency
Canada
Stephen E. Weber
Centers for Epidemiology and Animal Health
Fort Collins
United States of America
Armando Giovannini
Istituto Zooprofilattico Sperimentale dell’Abruzzo e del Molise,
Italy
David Wilson
Head
International Trade Department
OIE, France
Acknowledgments
This second volume of the OIE Handbook on Import Risk Analysis: Animals and Animal
Products draws heavily on David Vose’s Risk Analysis: A Quantitative Guide (John Wiley &
Sons, Chichester. 2000). Vose’s book is an indispensable reference text for both the student and
practitioner of animal health risk analysis. The text also draws on the book Import Risk Analysis:
Animals and Animal Products (2002) by Noel Murray, published by the Biosecurity Authority,
Ministry of Agriculture and Forestry, New Zealand.
Various people have offered critical comment on all or part of the modified text. In particular the
Author and Editors wish to acknowledge:
David Vose
David Vose Consultancy
www.risk-modelling.com
Michael Roberts
Neil Cox
AgResearch Ltd
New Zealand
Lisa Gallagher
Tracey England
Louise Kelly
Rowena Jones
Veterinary Laboratories Agency (Weybridge)
United Kingdom
Sanping Chen
Carleton Quantitative Research
Ottawa
Canada
IV Handbook on Import Risk Analysis for Animals and Animal Products, Volume 2, 2004
Anna Maria Conte
Istituto Zooprofilattico Sperimentale
dell’Abruzzo e del Molise,
Italy
Ziad A. Malaeb
Centers for Epidemiology and Animal Health
Fort Collins
United States of America
The Author and Editors thank Professor Vincenzo Caporale, Director of the OIE Collaborating
Centre for Epidemiology and Organization of Veterinary Services in Developing Countries,
Istituto Zooprofilattico Sperimentale dell’Abruzzo e del Molise, Teramo, Italy, for hosting their
meetings and providing secretarial services during the drafting of the text.

_____________

Handbook on Import Risk Analysis for Animals and Animal Products, Volume 2, 2004 V

Chapter 1 : An introduction to quantitative risk analysis
Chapter 1
An introduction to quantitative risk analysis1
Introduction
In Volume 1 of this Handbook we stated that no single method of import risk assessment
has proven applicable in all situations, and different methods may be appropriate in
different circumstances2. In qualitative assessments, the likelihood the release and
subsequent exposure to a hazard and the magnitude of the resulting consequences are
expressed using non-numerical terms such as high, medium, low or negligible, and the
qualitative approach has so far proved suitable for the majority of import risk assessments.
However, in some circumstances it may be desirable to undertake a quantitative analysis,
for example, to gain further insights into a particular problem, to identify critical steps or to
compare sanitary measures.
The terms ‘parameter’, ‘variable’, ‘input’ and are often used interchangeably in quantitative
risk assessments. In this Handbook, these terms are used as follows:
– Parameter
In experimental statistics the term parameter represents a numerical descriptive measure
that characterises a population, for example the population mean (), the population
standard deviation () and the binomial proportion (p). In spread sheet computer
software, it is often used to represent the arguments of mathematical, statistical or
probability distribution functions such as the values required to define the shape of a
Beta distribution or the mean and standard deviation of a normal distribution.
– Variable
A variable is any characteristic that has a different value for different subjects or objects.
If it can take on a different value as a result of a random process it is called a random
variable. It can either be discrete, where it can only take on a limited number of values,
or continuous, where it can take on any value within a given range. Examples of discrete
variables include the number of infected animals, the number of test positive animals or
the number of piglets in a litter, while examples of continuous variables include
bodyweight or blood copper levels.
– Inputs
An input is any information that is fed into a model. As a result parameters and
variables, together with data and distributions, can be considered as inputs as they
provide information that is used in a quantitative risk assessment model.
– Model
A model is a simplified representation of the real world. Most models are symbolic
because symbols represent properties of the system. In this handbook, a ‘model’ is a
representation of an importation scenario in graphical or mathematical form where

1 The general reference for this chapter is Vose D. (2000). – Risk Analysis, A Quantitative Guide. John Wiley & Sons
Chichester.
2 Terrestrial Animal Health Code, Article 1.3.1.1
Handbook on Import Risk Analysis for Animals and Animal Products, Volume 2, 2004 1
Chapter 1 : An introduction to quantitative risk analysis
equations are used to simulate the biological processes under study and the impact of
risk management options.
– Quantitative risk assessment
A quantitative risk assessment is a mathematical model where the inputs and outputs are
expressed numerically. In its simplest form, commonly referred to as a deterministic or
point estimate analysis, both the inputs and outputs are expressed as single numbers or
point values. These may represent a ‘best guess’, the ‘average’ or ‘expected case’ or
perhaps the ‘worst case’. When one wants to determine the impact of one or more of
the input values on the output, one simply substitutes a new value into the model. This
is effectively a ‘what if’, or scenario, analysis. For simple models with few inputs, this
type of analysis can be easily undertaken using a calculator.
For more complex models, or in situations where one has more data to work with,
probabilistic risk assessments are preferable. In these, inputs are described as probability
distributions and a computer is essential for constructing the risk assessment model.
Deterministic (point estimate) risk assessment
Quantification of risk begins with considering an experiment, or trial with only two
possible outcomes: success or failure. The trial may be repeated a number of times. For
example, a trial may be a single embryo transfer from an infected animal to a susceptible
recipient. A ‘success’ in this case would be where the infection is transmitted while a
‘failure’ would be a transfer where infection is not transmitted. If we observe no successes
after ten transfers (trials) we may begin to suspect that the probability of transmitting
infection by embryo transfer is low. As more transfers are undertaken without transmitting
infection, the more confident we become that transmission is unlikely. This is shown in
Table I, where confidence intervals3 have been determined by consulting the statistical
tables presented in Appendix 1.
Table I
Probability of transmitting infection following embryo transfer from a viraemic
donor
Number of Number of Probability of transmitting Lower 95% Upper 95%
transfers (n) infected infection  r  confidence confidence
p   100 
recipients I t N  limit limit
10 0 0.00 0.00 30.85
20 0 0.00 0.00 16.84
30 0 0.00 0.00 11.57
40 0 0.00 0.00 8.81
100 0 0.00 0.00 3.62
1,000 0 0.00 0.00 0.37
If 100 experimental transfers were undertaken without transmitting infection, we could
reasonably conclude, using the upper 95th percent confidence interval, that the probability

3 A confidence interval is a range of numbers believed to include an unknown quantity with a specified level of
confidence. For example, if we weighed 10 sheep we could calculate their average weight and the associated confidence
intervals. If the average weight is 50 kg and the 95% confidence interval is  2.5 kg, this indicates that we could be 95%
confident that the true average weight of all sheep in the flock lies somewhere within the interval bounded by 47.5 kg and
52.5 kg
2 Handbook on Import Risk Analysis for Animals and Animal Products, Volume 2, 2004